Projectile motion

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Projectile motion

• X meets Y and a beautiful dance ensues often
  leading to great destruction.

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Projectiles

• A projectile has only one force acting upon - the
  force of gravity
• Examples golf, soccer ball, bullet, rock
  dropped, javelin thrower

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The path (trajectory)of a projectile is a
parabola
Parabolic motion of a projectile
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Horizontal and vertical motion are independent
(90)

• There are the two components of the projectile's
  velocity horizontal vX and vertical vY .
• The horizontal component of its velocity does
  not change. vX is constant

Gravity is the only force
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Horizontal and vertical motion are independent !
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Package drop

• The package follows a parabolic path and remains
  directly below the plane at all times
• The vertical velocity changes (faster, faster)
• The horizontal velocity is constant!

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Trajectory and Range

• Maximum range is at 45
• Low and high trajectory cover the same distance.
• 30 and 60
• 10 and 80
• 25 and

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• Projectile motion Animation
• http//www.ngsir.netfirms.com/englishhtm/ThrowABal
  l.htm
• QT movie
• http//www.physicslab.co.uk/shoot.htm

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vX is constant vy changes
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Component of Motion Equation
X Acceleration                    
Y Acceleration                        
X Velocity                               
Y Velocity                                            
X Position                                      
Y Position                                                 

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History of science

• Projectile motion based on Aristotelian
  principles.

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"Four Mortars Firing Stones into the Courtyard of
a Fort" (c.1504), by Leonardo da Vinci
(1452-1519)
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Projectile motion depicted in Nova Scientia
(1537), by Niccolò Tartaglia (c.1500-1557)
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"Judith Slaying Holofernes" (c. 1620), by
Artemisia Gentileschi (1593-1652)
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A Treatise of the System of the World (published
posthumously, 1729) by Isaac Newton (1642-1727)
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                               General 1-D
Velocity Equation                            
                              X-Component of
Velocity                                     
                                                  
     Y-Component of Velocity
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Projectile motion at an angle

• Time for Peak of Projectile
• Maximum height
• Maximum Range
• Velocity and Position Equations using Angular
  Dependence

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Experiment
What do you think? Which ball will hit the ground
first? a) The left ball will hit firstb) The
right ball will hit firstc) They will hit the
ground at the same time.
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Projectiles
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Both balls hit the ground at the same time. Why?

• As soon as both balls are released by the
  launcher, they are in "freefall.
• The only force acting on both objects is gravity.
• Both objects accelerate at the same rate, 9.8m/s2
• Both objects covering the same distance at the
  same rate and therefore hit the ground at the
  same time
• d ½ gt2 t2 2d/g

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Shoot the monkey!
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Projectile
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Circular Motion Principles for Satellites
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Satellites

• Sputnik 1958

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• Satellites can be classified by their functions.
  Satellites are launched into space to do a
  specific job.
• (Astronomy, weather, communication, navigation,
  remote sensing, space exploration)

http//collections.ic.gc.ca/satellites/english/eng
ineer/copy/index.html
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Orbits

• After a satellite is launched into space, it
  needs little to no power to keep it moving
• The orbit is a combination of the satellite's
  velocity - the speed it is traveling in a
  straight line - and the force of the Earth's
  gravitational pull on the satellite.

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• Communication satellites, TV
• High orbit - 35, 850 km above the Earth
• located directly above the equator -equatorial
  orbit
• G.E.O. which stands for Geostationary Orbit.
• Geostationary satellites like geosynchronous
  satellites take 24 hours to complete a rotation.

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• Low Earth Orbit, or L.E.O.  L.E.O. is 248 to 621
  miles high from earth. L.E.O. is good for
  weather, survey and scientific satellites.
• There is also the P.O. which is the Polar Orbit.
  Polar Orbit is another low earth orbit used for
  mapping, navigation and surveillance.
• http//science.nasa.gov/realtime/
• http//www.lon-capa.org/mmp/kap7/orbiter/orbit.ht
  m